RESEARCH ARTICLE

VOLCANS: an objective, structured and reproducible methodfor identifying sets of analogue volcanoes

Pablo Tierz1,2 & Susan C. Loughlin1& Eliza S. Calder2

Received: 23 February 2019 /Accepted: 8 November 2019# The Author(s) 2019

AbstractThe definition of a suite of analogue volcanoes, or volcanoes that are considered to share enough characteristics as to be consideredexchangeable to a certain extent, is becoming a key component of volcanic hazard assessment. This is particularly the case forvolcanoes where data are lacking or scarce. Moreover, volcano comparisons have often been based on similarities and differencesinferred through expert judgement and not necessarily informed by volcano characteristics from global datasets. These similaritiescan be based on a range of features, from very simplified (e.g. statrovolcanoes) to very specific (e.g. detailed eruption chronologies),and may be strongly influenced by the personal experience of individuals or teams conducting the analogue analysis. In this work,we present VOLCANS (VOLCano ANalogues Search)—an objective, structured and reproducible method to identify sets ofanalogue volcanoes from global volcanological databases. Five overarching criteria (tectonic setting, rock geochemistry, volcanomorphology, eruption size and eruption style), and a structured combination of them, are used to quantify overall multi-criteriavolcano analogy. This innovative method is complementary to expert-derived sets of analogue volcanoes and provides the user withfull flexibility to weigh the criteria and identify analogue volcanoes applicable to varied purposes. Some results are illustrated forthree volcanoes with diverse features and significant recent and/or ongoing eruptions: Kıl̄auea (USA), Fuego (Guatemala) andSinabung (Indonesia). The identified analogue volcanoes correspond well with a priori analogue volcanoes derived from expertknowledge. In some cases, single-criterion searches may not be able to isolate a reduced set of analogue volcanoes but any multi-criteria search can provide high degrees of granularity in the sets of analogue volcanoes obtained. Data quality and quantity can beimportant factors, especially for single-criterion searches and volcanoes with very scarce data (e.g. Sinabung). Nevertheless, themethod gives stable results overall across multi-criteria searches of analogue volcanoes. Potential uses of VOLCANS range fromquantitative volcanic hazard assessment to promoting fundamental understanding of volcanic processes.

Keywords Global volcanism . Global database . Volcano morphology . Volcanic hazard assessment . Scarce data . Objectiveanalogue volcano

Introduction

Volcanoes are powerful manifestations of our geodynamicplanet. Volcanic physico-chemical processes are extraordinarily

complex and operate on spatial and temporal scales rangingover many orders of magnitude (Sigurdsson et al. 2015).Therefore, volcanic behaviour is truly challenging to under-stand and even more challenging to forecast. Volcano scientistsworldwide are asked, on a daily basis, to collect, process andinterpret varied types and sources of volcanological data (e.g.deposits of volcanic material, chemical compositions of volca-nic minerals and rocks, seismic signals from volcano-tectonicearthquakes, ground deformation, gas emissions) for its use inforecasting the future short- and long-term evolution of a par-ticular volcanic system (e.g. Newhall and Hoblitt 2002;Loughlin et al. 2015; Newhall et al. 2017). Some frequentlyactive volcanoes may appear somehow predictable (e.g.Stromboli, Italy), due to the fact that they tend to behave asthey have behaved in the past (e.g. Blackburn et al. 1976; Rosi

Editorial responsibility: C.E.Gregg

Electronic supplementary material The online version of this article(https://doi.org/10.1007/s00445-019-1336-3) contains supplementarymaterial, which is available to authorized users.

* Pablo Tierzpablo@bgs.ac.uk

1 British Geological Survey, The Lyell Centre, Edinburgh, UK2 School of Geosciences, University of Edinburgh, Edinburgh, UK

Bulletin of Volcanologyhttps://doi.org/10.1007/s00445-019-1336-3

(2019) 81: 76

Published online: 6 December 2019/

et al. 2000; Taddeucci et al. 2015). Yet, this by no means ex-cludes relatively rapid changes in behaviour towards less ex-pected phenomena: e.g. paroxysmal activity at Stromboli (e.g.Bertagnini et al. 2003; Calvari et al. 2006; Aiuppa et al. 2010),of which the 3 July and 28 August 2019 explosions were apowerful reminder. Other frequently active volcanoes mayshow more complex behaviours, such as switching betweenopen-conduit (i.e. magma is filling the conduit below the craterand feeds the eruption) and closed-conduit regimes (i.e. theconduit is plugged by a semi- or totally-crystallysed rock).Some volcanoes may erupt frequently enough that sufficientdata can be collected to postulate qualitative or quantitativeforecasting models of volcanic activity (e.g. Volcán deColima, Mexico; Luhr and Carmichael 1990; De la Cruz-Reyna 1993; Luhr et al. 2002). Volcanoes that erupt infrequent-ly and/or have very few data available concerning past behav-iour are more numerous: Loughlin et al. (2015) estimated thatabout 70% of the world’s Holocene (last ~ 12 kyr) volcanoesare very poorly studied. These volcanoesmay show no eruptivesigns for centuries and, therefore, go unnoticed by local popu-lations but they may, in a matter of weeks to months, growrestless and produce energetic eruptions. For instance, MountPinatubo (Philippines), erupted in 1991 after approximately500 years of repose, in what was the second largest eruptionof the 20th century (Newhall and Punongbayan 1996). Thesepoorly-studied, potentially dangerous volcanoes are one majorreason why the volcanological community has sought to iden-tify analogue volcanoes, which are volcanoes believed to sharesome commonalities in terms of their specific “type, magmacomposition, repose period, or any other characteristics of in-terest” (Newhall et al. 2017).

Volcano observatories and crisis-response teams world-wide, such as the Volcano Disaster Assistance Program ofthe United States Geological Survey (https://volcanoes.usgs.gov/projects/VDAP/about.html), have been using analoguevolcanoes to inform their volcanic hazard assessments overthe last decades, which has helped protect communitiesliving around active volcanoes in many countries around theworld (Sandri et al. 2012; Ogburn et al. 2015; Newhall andPallister 2015; Newhall et al. 2017). More broadly, analoguevolcanoes have been identified for the purpose of classifica-tion (Hone et al. 2007) or, in general, to improve hazard as-sessments at different temporal and spatial scales (Marzocchiet al. 2004; Mastin et al. 2009; Sandri et al. 2012; Whelleyet al. 2015). Table 1 contains a summary of previous studieson analogue volcanoes, the purpose of the analysis and thecriteria that have been most commonly used to define sets ofanalogue volcanoes.

Volcano types are usually grouped according to classicalstratovolcanoes (Sheldrake 2014) or calderas (Sobradelo et al.2010; Acocella et al. 2015) but more detailed analyses ofgeomorphological features have also been proposed(Whelley et al. 2015). Geographic setting has been used to

ensure homogeneity between sets of volcanoes (Bebbington2014) and it sometimes corresponds well with broad classes oftectonic setting (Hone et al. 2007; Whelley et al. 2015).Similarity in magma composition is typically described bysimple geochemical divisions (e.g. mafic/felsic or basalt/an-desite/dacite/rhyolite, Hone et al. 2007; Mastin et al. 2009;Ogburn et al. 2015), but more elaborate schema may includerock affinity (e.g. tholeiitic/calc-alkaline/alkaline, Sobradeloet al. 2010). In terms of (explosive) eruption size and style,Volcanic Explosivity Index (VEI, Newhall and Self 1982) is acustomary choice (Bebbington 2014; Ogburn et al. 2015) buta great variety of more-or-less specific metrics have beenused. These include the following: repose period, open/closed conduit, mass eruption rates, grain size distribution,lava-dome-growth durations and extrusion rates and genera-tion of specific types of pyroclastic density currents (PDCs)(Marzocchi et al. 2004; Mastin et al. 2009; Sandri et al. 2012,2014; Sheldrake 2014; Ogburn et al. 2015).

Classically, analogue volcanoes are identified by classi-fying volcanoes into isolated compartments or categories(e.g. andesitic stratovolcanoes that generate dome-collapsePDCs). At high levels of detail, the number of categoriescan be very large and volcanoes become seemingly unique(Cashman and Biggs 2014). Consequently, the identifiedsets of analogue volcanoes may be suited for a given spe-cific problem but wider applicability of the methods andresults is prevented. In addition, the common practice inchoosing analogue volcanoes is almost purely based on thepersonal experience or knowledge of the hazard analyst orteam. The selection of analogue volcanoes under such cir-cumstances may be significantly biased by specific erup-tion behaviour patterns known from a handful of volcanoesrather than from global databases.

In this study, we develop an objective, structured and re-producible method for identifying sets of analogue volcanoesbased on information from three global volcanological data-bases. We refer to this tool as VOLCANS (VOLCanoANalogues Search). Different criteria (tectonic setting, rockgeochemistry, volcano morphology, etc.) are used to quantifyeither single-criterion or multi-criteria volcano analogy, whichis interpreted as the inverse of a distance metric defined be-tween any two volcanic systems in the databases. This dis-tance metric is a proxy for dissimilarity and is calculated usingnormalised numerical variables, which provides a quantifica-tion of the volcano analogy between zero and one. This gen-erates a continuum of possible analogue volcanoes and givesthe method considerable flexibility in scope and application.First, an automated quantitative procedure to identify sets ofanalogue volcanoes offers an accountable and reproduciblemeans to use these sets to support improved hazard assess-ments worldwide. Second, objective provision of analoguesets can also contribute new insight into the study of funda-mental magmatic or physical volcanic processes where that

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understanding is built on the observation of commonalitiesacross individual volcanic centres. Third, data-derived an-alogue volcanoes can become a powerful complement tosets of analogue volcanoes obtained through expert knowl-edge (e.g. Marzocchi et al. 2004; Sandri et al. 2012, 2014;Newhall and Pallister 2015). Nevertheless, it is crucial tonote that a careful use of those sets of automatically-derived analogue volcanoes is necessary. The user needsto have a clear understanding of how the sets are gener-ated and the significance and relevance of the analoguevolcanoes obtained has to be assessed in the specific con-text of each analysis.

In the following, the source datasets and methods used todefine volcano analogy are described. Then, VOLCANS isdemonstrated through results for three volcanoes that (1) havecharacteristics that span across the different criteria (e.g.intraplate/subduction zone, basalt/andesite/dacite, shield vol-cano/stratovolcano); (2) have been studied to different levelsof detail (i.e. some are data-rich, others are not); and (3) haverecently experienced major phases of volcanic activity. Thethree volcanoes are as follows: Kıl̄auea, USA (intense phaseof rifting and lava effusion from April to August 2018,approximately; Global Volcanism Program 2013, Neal et al.2019); Fuego, Guatemala (significant explosion anddevastating PDCs on 3 June 2018, Naismith et al. 2019);and Sinabung, Indonesia (long-term eruption from 2013 to2018, and new phase starting in May 2019, with numerousPDCs and some large explosions; Global Volcanism Program2013; Gunawan et al. 2019). Finally, the main applications

and limitations of VOLCANS, including potential issues withthe source datasets, are discussed.

Source datasets

The three global volcanological databases used are as follows:(1) the Holocene Global Volcanism Program database (GlobalVolcanism Program 2013, version 4.6.7), hereinafter GVP; (2)the volcano morphology database of Pike and Clow (1981),hereinafter Pike81; and (3) the volcano morphology databasepresented by Grosse et al. (2014), hereinafter Grosse14. Forthe Pike81 and Grosse14 databases, only the data correspond-ing with volcanoes with a unique identifier matching onto theGVP database are used. Moreover, the two morphologicaldatabases are merged into a unique dataset, by assessing thecorrespondence and exchangeability between the variablesfound in each of the databases (see Online Resource 1 formore details). CSV files containing all datasets used in theanalysis can be found in Online Resources 2, 3, 4 and 5.

Global Volcanism Program database

The GVP database is the global reference for the list ofHolocene and Pleistocene volcanic systems in the world, butin this work, only the Holocene list is used. The GVP storesinformation for any volcanic system with known or suspectederuptive activity during the last 12 kyr, approximately. Thedata are publicly available and can be downloaded in XMLformat via four different searches: volcano, eruption,

Table 1 Previous studies that used sets of analogue volcanoes for different purposes (see first column). The main criteria which served to identify thesesets are indicated. The last row displays the number of studies that used each criteria, out of the total number of studies shown

Use of analysis Volcano type Geographicarea

Tectonic setting Magmacomposition

Eruptionsize/style

Type ofunrest

Reference

Hazard assessment X X Marzocchi et al. (2004)

Volcano classification X X X X Hone et al. (2007)

Hazard assessment X X Mastin et al. (2009)

Volcano classification X X X Sobradelo et al. (2010)

Hazard assessment X X X Rodado et al. (2011)

Hazard assessment X X Sandri et al. (2012, 2014)

Hazard assessment X X Bebbington (2014)

Hazard assessment X Sheldrake (2014)

Analysis of unrest X X Acocella et al. (2015)

Hazard assessment X X X Ogburn et al. (2015)

Hazard assessment X X X Whelley et al. (2015)

Hazard assessment X X Tierz et al. (2016a)

Analysis of unrest X X X X Newhall et al. (2017)

10/13 3/13 2/13 7/13 10/13 1/13

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deformation and emission. Data from the volcano and erup-tion searches are used in this study. This includes informationabout volcano name, type, tectonic setting, major and minorrock types, VEI sizes of eruptions and eruptive phenomena.(see Online Resources 2, 3, 4 and 5).

Pike and Clow (1981) database

This database contains the topographic dimensions of terrestrialand some planetary volcanic systems, in particular the height,flank width, and diameter, depth and circularity of the summitdepression, which sometimes corresponds to a crater and othersto a caldera. The database has information for volcanoes of anytype (Grosse14 does not have calderas), but the measurementswere performed manually from diverse maps or aerial photo-graphs. Therefore, if a volcano in the Pike81 database has anequivalence available in the Grosse14 database, the lattersource, which is more accurate and less subjective, is used.

Grosse et al. (2014) database

The Grosse14 database contains different morphological var-iables relating to the edifice (height, width, average slope, etc.)and, in some cases, to the summit depression (depth, width,ellipticity, etc), derived using a common topographic source(Digital Elevation Models derived from the Shuttle RadarTopographyMission, with spatial resolution of 90m) andwithdeveloped algorithms that automatically define parameterssuch as the lateral extent of the volcanic edifice (Grosseet al. 2012; Euillades et al. 2013). Only positive-relief volca-noes are included in the database (predominantly shields andstratovolcanoes). Hence, caldera systems are retrieved fromthe Pike81 database.

Methods

The goal of VOLCANS is a quantification of single-criterionand multi-criteria analogy between volcanic systems around theworld by means of five criteria, for which data for the majorityof volcanoes are available in the aforementioned databases(Figs. 1 and 2): (1) tectonic setting, (2) rock geochemistry, (3)volcano morphology, (4) eruption size and (5) eruption style.Analogy is understood to be a measure of similarity and, thus,the more similar two volcanic systems, the more analogous theyare. To measure this similarity, a distance metric, which rangesfrom zero to one, is defined for each analogy criterion (Table 2).The inverse of the distance metric represents the measure ofsingle-criterion analogy between any two volcanoes, and it alsoranges from zero to one. If the analogy is equal to zero, there isno analogy between the volcanoes. If the analogy is one, thevolcanoes are interpreted to be perfect analogues, for that par-ticular criterion. If a volcano X has a higher value of analogy

with volcano Y than with volcano Z, the interpretation is thatvolcano Y is a better analogue of volcano X than volcano Z.

In order to define each distance metric, categorical vari-ables (e.g. tectonic setting) are converted into numerical var-iables by applying sub-criteria which are deliberately indepen-dent of other sub-criteria and criteria. In other words, the def-inition of these numerical variables, and therefore the defini-tion of analogy for each criterion, is fully independent of anyother criteria (Table 2). For instance, magma geochemistry isnot considered when defining the analogy in morphology(Pike 1978; Pike and Clow 1981). Only edifice dimensionsare used to define such single-criterion analogy (Fig. 2). Fornumerical variables associated with a distribution instead of asingle value (e.g. VEI class), the distance metric is the areabetween the empirical cumulative distribution functions(ECDFs) of any two volcanoes (Fig. 1, Table 2). Finally, foreruption style, the distance metric is calculated as the normal-ised sum of differences in the unit proportion of eruptions thatgenerated diverse hazardous processes (e.g. lava flows andtephra fallout) at each volcano (Fig. 1, Table 2).

To quantify the overall analogy among any two volcanoes,X and Y, single-criterion analogies are combined into a multi-criteria analogy metric (AXY) using the following formula:

AXY ¼ wTs � ATsXY þ wG � AGXY þ wM � AMXY þ wSz

� ASzXY þ wSt � AStXY ð1Þ

where wi are the weights given to each single-criterionanalogies (Ts: tectonic setting, G: rock geochemistry, M: vol-cano morphology, Sz: eruption size, St: eruption style; seeTable 2). Note that some weights can be set to zero, in whichcase the corresponding single-criterion analogy is not consid-ered to calculate the multi-criteria analogy. Provided that thesum of weights equals one, the multi-criteria analogy metric isa weighted average of the single-criterion analogies betweenvolcanoes X and Y. If a given volcano has no data availablefor a given criterion, the single-criterion analogy between thisvolcano and any other volcano in the database is set to zero.This is a way to avoid calculating spurious volcano analogies:even if the analogy could exist, it is not possible to corroboratethis without any data available.

Analogy in tectonic setting

Given the small number of pseudo-quantitative categoriesused to describe tectonic setting in the GVP database, twosimplified sub-criteria are used to create a variable for tectonicsetting, Ts (Fig. 1a and Table 2). These criteria are linked to (a)the primary melting mechanism of the mantle (i.e. chemicallyversus decompression-driven); and (b) the easiness of the paththat the magma must traverse before it reaches the Earth’s

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surface (Pearce 1996; Perfit and Davidson 2000). That is, it isassumed that the shallower the melting depth and the thinnerthe lithosphere in/above the melting zone, the easier the pathtowards eruption (Fig. 1a). Consequently, low values of thevariable Ts correspond with decompression-driven (rifting)magmatism over more or less thin crust while high values ofthe Ts variable correspond with subduction-zone magmatismover more or less thick crust.

Analogy in rock geochemistry

Simplified versions of the two main geochemical/compositional diagrams to classify volcanic rocks are usedto define a variable for rock geochemistry, G (Total AlkaliSilica, TAS, and Quartz, Alkali feldspar, Plagioclase,Feldspathoid, QAPF diagrams; Le Maitre et al. 2005; Fig.1b). Hereinafter, the rock-type abbreviations used are the sameas in the GVP database (Siebert et al. 2010; GVP 2013).According to the position in the diagrams of a given rock typecompared with another rock type, a value of distance isassigned to the pair of rock types as follows: one if the rocktypes are adjacent; two if they are separated by one rock type,or three if they are separated by two different rock types. The

sum of the values from each diagram and for each pair of rocktypes ij is expressed as rij. It is a proxy for the dissimilaritybetween each pair of rock types: the higher the number, themore dissimilar the rocks. The numerical variable for rockgeochemistry (G) is defined to have as extreme points: (1)the most dissimilar rock in comparison with all the other rocks(i.e. the one with the highest sum of rij, over all j rock types):rhyolite, R; and (2) the rock type that is the most dissimilarcompared with rhyolite: i.e. foidite, F. Among the other eightrock types, the ones with the lowest value of rRj (dacite, D, andtrachyte, T) and rFj (tephrite/basanite/trachybasalt, X, phono-tephrite/tephri-phonolite, Z, and phonolite, P) are constrainedto be the closest rock types to rhyolite and foidite, respectively.Then, all possible arrangements of rock types (around 4500possible combinations) are explored to define the variable forrock geochemistry. The combination that minimises the totalsum of rij values among all the neighbouring rock types in thevariable is the one selected. The ordering of the rock types is:F-P-T-Y-Z-X-B-A-D-R (Fig. 1b), which reflects differences inSiO2, total alkali (NaO2 + K2O) and mineral contents betweenthe rock types. Indeed, the scale divides the subalkaline/tholeiitic (high values of the variable G) and alkaline rockseries (low values of the variable G). That is, B-A-D-R are

Fig. 1 Schematic showing themethodology used to define anddetermine quantitative metrics ofsingle-criterion analogy for (a)tectonic setting, (b) rock geo-chemistry, (c) eruption size and(d) eruption style. All metrics arebased on the inverse of the dis-tance between any two volcanoes(X, Y), according to the differentcriteria (see Table 2 and text formore details). Abbreviations: R.:Rift; Ip.: Intraplate; S.:Subduction; rock abbreviations asin Table 4 of Siebert et al. (2010);VEI: Volcanic Explosivity Index;Qtz: quartz; Or: orthoclase; Pl:plagioclase; Foid: feldspathoid;hiX: frequency of eruptions of

volcano X for which the ith haz-ardous process has been reported;hiY: frequency of eruptions of

volcano Y for which the ith haz-ardous process has been reported;H: total number of groups ofhazardous processes; WSF:water-sediment flow; PDC: pyro-clastic density current

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closer to each other in comparison to the other, more alkali-rich rock types, as reported by Le Bas et al. (1986). However,it must be noted that the geochemical data for many volcanoesin the GVP database may come from general rock definitions(e.g. basalt or andesite) that do not differentiate betweensubalkaline and alkaline rock suites (Siebert et al. 2010).

In order to account for intra-volcano geochemical variabil-ity, all major and minor rock types in the GVP database areconsidered, for any given volcano. Each major rock type iscounted as two data points and each minor rock type as one

data point to create normalised histograms and ECDFs of rocktypes, one for each volcano. The measure of single-criterionanalogy for rock geochemistry between volcanoes X, Y, is theinverse of the area between their ECDFs (Fig. 1b). In otherwords, it is a measure of the overlap between the histogramsof rock types for volcanoes X, Y (Fig. 1b, Table 2).

Analogy in volcano morphology

Volcano morphology is derived based on (Fig. 2) crater/caldera diameter (d), height of rim crest above pre-volcanotopography (H), ratio between the height and half-width ofthe volcanic edifice (H/W*) and truncation parameter of thevolcanic edifice (T~d/2W*). The values of all of these vari-ables have been checked to be consistent and compatibleacross the two volcano morphology databases (see OnlineResource 1).

Based on its ECDF, each variable is divided into 10-percentiles-wide classes or ranks. Each rank is assigned a val-ue from 1 (i.e. 0–10th percentiles) to 10 (i.e. 90–100th per-centiles). In Fig. 2b, the values of each rank for a given vari-able are plotted against the mean value of the rank for anothervariable. This shows the general underlying trends betweenthe different variables, without these trends being obscured bythe dense continuum of morphologies that exist in the world’svolcanoes (Grosse et al. 2014). Small values of d and T tend tooccur together with high values ofH andH/W* (Fig. 2b). Thiscorresponds well with the view of high volcanic edifices (e.g.stratovolcanoes) having high height-to-width ratios, small cra-ters and relatively low truncation values (Grosse et al. 2009,2014). On the contrary, low-altitude edifices (e.g. shields andcalderas) are commonly conceived to have low height-to-width ratios, large craters/calderas and sometimes high trun-cation (Pike 1978; Pike and Clow 1981). The merged datasetused here confirms these trends. Therefore, the morphology ofa volcano is described by variable M:

M ¼ d þ T– H þ H=W*ð Þ ð2Þwhere d, T, H, H/W* correspond to the aforementioned rankvalues (from 1 to 10), for any given volcano. The M variableseparates volcanoes that have low-height, gentle-slope,highly-truncated edifices with large craters (high values ofM) from volcanoes that have high, steep-slope, low-truncation edifices with small craters (low values of M). Allentries in the merged morphology database have an entry forthe variables T, H and H/W*. However, some of the stratovol-canoes taken from the Grosse14 database lack a measure ofthe variable d, most commonly linked with very small craters(Grosse et al. 2014). In such cases, a rank value of zero is used.

Figure 2c shows the distributions of M values obtainedwhen grouping volcanic systems according to their Primary

Fig. 2 Derivation of a unified variable (M) to measure volcanomorphology: (a) schematic showing the dimensions of the volcanicedifice and the formula used to calculate M; (b) trends in thedimensions of volcanic edifices according to the morphologicaldatabases of Pike and Clow (1981) and Grosse et al. (2014); the graphson the columns show the rank value (x-axis) for the variable indicated oneach column against the mean rank value (y-axis) for the variable indi-cated on each row. d: crater diameter; H: height of rim crest above pre-volcano topography; W*: half width of the volcano; T: truncation of theedifice; (c) probability distributions ofM (non-normalised) for four clas-ses of Primary Volcano Types (a variable in the GVP database)

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Volcano Type defined in the GVP database. The distributionsof M for simple and complex/compound stratovolcanoes,shield volcanoes and caldera systems are significantly differ-ent (Fig. 2c). Table 3 reports the mean values ofM for all thesemain groups. Given the consistent separation of volcano typesin different populations of the M variable (Fig. 2c), meanvalues of M are assigned to all the GVP entries that are notdescribed in the merged morphological database but that areclassified as stratovolcanoes, shields or calderas by the GVPdatabase according to their Primary Volcano Type. In the caseof volcanic fields, a (normalised) value of M = 1 is assigned,this being purely based on their general morphology, whichfeatures large lateral extension and very limited verticalextent.

Analogy in eruption size

For volcanoes with an eruption record in the GVP database,the volcano analogy in terms of eruption size and eruptionstyle is assessed. The approach of merging the whole recordeddataset of eruption sizes and hazardous phenomena for anygiven volcano assumes stationarity in activity, at least whenaveraged over the Holocene. Nonetheless, it is acknowledgedthat analyses of the eruptive histories at individual volcanoesover shorter periods of time commonly evidence non-stationary behaviours (e.g. Bebbington 2008; Marzocchi andBebbington 2012; Connor et al. 2015).

Given that VEI 2 is the default assignment in the GVPdatabase and the fact that effusive (VEI 0) and very smallexplosive eruptions (VEI 1–2) are particularly under-reported (De la Cruz-Reyna 1991; Mead and Magill 2014),all eruptions with VEI ≤ 2 are grouped together (Mead andMagill 2014). Under-recording issues are expected to affect

any analysis of frequency-size of eruptions, independently ofwhether VEI or eruption magnitude data are used (Rougieret al. 2016). A simplified approach to compensate for under-recording is implemented: (1) a suitable function to model theprobability of recording an eruption of a given VEI x, at time t,is identified; and (2) this probability is used to extrapolate thenumber of eruptions of that VEI that might have been missedat the specific volcano. Thus, the total number of eruptions ofa given VEI (x) that have occurred at a given volcanic systemis estimated as:

ER xð Þ ¼ ER1 xð Þ þ ER2 xð Þ ð3Þwhere ER1(x) denotes the total number of eruptions of VEI xthat occurred before the date of completeness (k, considered asthe date after which the recording probability is one; MeadandMagill 2014) and ER2(x) denotes the total number of erup-tions of VEI x that occurred after the date of completeness k.For each volcano and eruption size, if ER(x) is not an integer,its value is rounded to the closest integer. ER2(x) is calculateddirectly from summing up the number of recorded eruptions inthe GVP database, for a given volcano after time k, given thatthe recording probability is assumed to be one. ER1(x) is cal-culated as follows:

ER1 xð Þ ¼∑k

t¼t1Er1 t; xð Þp t; xð Þ ð4Þ

where p (t, x) is the recording probability of an eruption of VEIx that occurs at time t ≤ k and Er1 (t, x) denotes the indicatorfunction for any eruption of VEI x that occurred at time t ≤ k.

Table 2 Framework to define and determine single-criterion analogymetrics for five different volcanological criteria. “D” stands for the abso-lute distance between any two volcanoes (X, Y) within a given criterionand it is measured in slightly different ways for the different criteria (seealso Figs. 1 and 2). “A” stands for single-criterion analogy and it is theinverse of the distance “D”. Multi-criteria volcano analogy is defined as aweighted sum of single-criterion analogies (see Eq. (1) and text for more

details). TAS, total alkali silica; QAPF, Quartz-Alkali feldspar-Plagioclase-Feldspathoid; VEI, Volcano Explosivity Index; ECDF, em-pirical cumulative distribution function (letter “F” in the distance-metriccolumn is equivalent to ECDF); Ts, tectonic setting; G, rock geochemis-try; M, volcano morphology; Sz, eruption size; St, eruption style; hi,frequency of eruptions with a given hazardous phenomena i; H, totalnumber of groups of hazardous phenomena (see Table 4)

Criterion Sub-criteria Type of distance metric Distance metric Analogy metric

Tectonic setting Crustal thickness Linear DTsXY = |TsX − TsY| ATsXY = 1 − DTsXYMantle-melting mechanism

Rock geochemistry TAS diagram Area between ECDFs DGXY = |FGX − FGY| AGXY = 1 − DGXY

QAPF diagram

Volcano morphology Edifice height Linear DMXY = |MX − MY| AMXY = 1 − DMXY

Edifice height/half-width ratio

‘Crater’ diameter

Summit width/edifice width ratio

Eruption size Distribution of VEI sizes Area between ECDFs DSzXY = |FSzX − FSzY| ASzXY = 1 − DSzXYEruption style Grouping of hazardous phenomena Sum of frequency differences DStXY = (Σi

N |hXi − hYi|)/H AStXY = 1 − DStXY

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The sum of Er1 (t, x) is the total number of eruptions of size xrecorded before time k.

A single-change-point presence function is used to modelthe recording probability (Furlan 2010; Mead and Magill2014):

p t; xð Þ ¼1

1þ e−a−βx1

t≤kt > k

)(ð5Þ

where α, β are the parameters controlling the scale and shapeof the function. The date of completeness k is taken fromTable 1 in Mead and Magill (2014), in particular the medianvalue of the change point posterior distribution in their model,for any volcano in a given country. In the absence of data atthe country scale, the k value available for the correspondingregion is used.

The α and β parameters are selected following two naiveassumptions. Before the date of completeness: (a) VEI = 0eruptions are “exceptionally unlikely” (Mastrandrea et al.2010) to be recorded, i.e. p(t, 0) = 0.01; and (b) VEI = 8eruptions are “virtually certain” (Mastrandrea et al. 2010) tobe recorded, i.e. p(t, 8) = 0.99. It is noted that the latter mayactually be an overestimation given that around 70% of theworld’s Holocene volcanoes are very poorly studied(Loughlin et al. 2015). These two assumptions provide aparameterisation for the presence function in Eq. (5): α = −4.595, β = 1.150. Using this parameterisation, a VEI 4 erup-tion, for instance, has a 50% probability of being recorded,before the date of completeness k.

The choice of a single-change-point function can be ques-tionable at global scales (Deligne et al. 2010; Rougier et al.2016) but may be adequate for many countries and regions,especially for small-size eruptions (Jenkins et al. 2012) and/orfor those areas where geological data are scarce compared tohistorical data (Mead and Magill 2014). In our study, thischoice is a convenient one, given that all the eruptions thatoccurred at time t ≤ k can then be cumulated to estimate thetotal number of eruptions that might have happened over thattime span. This partially relaxes the issues of under-recordingin the GVP database.

Normalised VEI sizes are used as the variable for eruptionsize and the value of ER(x) at each volcano is used to build ahistogram, and an ECDF, which estimates the frequency-

magnitude distribution at each specific volcano (given erup-tion). The area between the ECDFs of any two volcanoes, Xand Y, is used as the distance metric for the eruption-sizecriterion. The associated single-criterion analogy is the inverseof this distance metric (Fig. 1c and Table 2).

Analogy in eruption style

In order to estimate single-criterion analogy in eruption style,data on hazardous phenomena are used. A total number of 22Event types from the GVP database are grouped into eightgroups of hazardous processes (Fig. 1d, Table 4, OnlineResource 1). At each particular volcano, the total number ofoccurrences of each group is divided by the total number oferuptions with eruption-style data, to calculate the proportionof eruptions that generated each group of hazardous phenom-ena. To avoid duplications, two or more events of the samegroup occurring during the same eruption are counted as onlyone occurrence of the group. The normalised sum of differ-ences between the proportions of the different hazardous pro-cesses is used as the distance metric for the eruption-styleanalogy between volcanoes X, Y (DStXY, Fig. 1b and Table 2):

DStXY ¼∑N

i¼1hXi −h

Yi

�� ��H

ð6Þ

where H is the total number of groups of hazardous phe-nomena, and hi

X and hiY are the frequencies of occurrence

(or proportions) for the ith group and volcanoes X and Y,respectively. Thus, the analogy in eruption style can beinterpreted as an average difference between the propor-tions of the different hazardous phenomena. It is also notedthat Eq. (6) penalises both differences in the frequency ofoccurrence and data scarcity in the groups of hazardousphenomena, for if there is no data for a given group, hi willbe equal to zero.

Results

The content and functionality of VOLCANS is illustrated byanalysing different sets of analogues for Kıl̄auea (USA),

Table 3 Summary of the minimum, maximum and mean values of the morphology variable (M) for simple, complex and all stratovolcanoes, shieldvolcanoes and caldera systems, all according to the assigment of “Primary Volcano Type” stored in the GVP database

Simple stratovolcanoes Complex stratovolcanoes All stratovolcanoes Shield volcanoes Calderas

Minimum M 0.000 0.105 0.000 0.158 0.447

Mean M 0.333 0.390 0.338 0.567 0.782

Maximum M 0.947 0.816 0.947 0.921 0.974

Bull Volcanol (2019) 81: 7676 Page 8 of 22

Fuego (Guatemala) and Sinabung (Indonesia). Figure 3 con-tains a summary of the ID profile of each volcano, that is, thedata available for each analogy criterion. Single-criterion andmulti-criteria analogies are described and top analoguevolcanoes (e.g. top 10 or top 20) are identified. In the caseof multi-criteria searches, three different weighting schemesare explored: (A) equal weighting, i.e. all criteria count thesame to calculate the volcano analogy, (B) eruption size andstyle are the only criteria used (equal weight between them)and (C) rock geochemistry and volcano morphology are theonly criteria used (equal weight between them). Theseweighting schemes, which explore the most-used criteria tosearch for analogue volcanoes (Table 1), are purely illustra-tive. The particular choice of weighting scheme, which obvi-ously alters the set of analogue volcanoes obtained, will de-pend on the specific goals and needs of each user. The signif-icant advantage of VOLCANS is that it provides the user withfull flexibility about this choice. Results revealed that somecriteria were non-differentiating while others weredifferentiating. Non-differentiating criteria are defined asthose that, for a specific volcano, result in tens or hundredsof analogue volcanoes with the same value of analogy (includ-ing one). Such criteria cannot be used to identify reduced sets

of analogue volcanoes. Differentiating criteria, on the otherhand, result in much fewer analogue volcanoes with the samevalue of analogy.

Kı̄lauea, USA

Kıl̄auea is a basaltic shield volcano located on an oceanicintraplate tectonic setting in relation to the presence of theHawaiian hot spot (Decker et al. 1987; Carey et al. 2015). Itformed on the eastern flank of the large Mauna Loa shieldvolcano at least 350 ka (Quane et al. 2000). Over the past200 yr, its eruptive products have mainly consisted of lavaflows but tephra layers have been also identified in thePleistocene and Holocene (Easton 1987; Fiske et al. 2009).In historical times, phreatomagmatic and phreatic explosiveeruptions have occurred (McPhie et al. 1990; Dvorak 1992;Mastin et al. 2004). Over a longer timescale of the past 2500yr, Swanson et al. (2014) identified several shifts betweenperiods dominated by either effusive or explosive volcanicactivity, each of those periods lasting for several centuries.Although erupted magma volumes were significantly higherduring effusive periods, the total duration of explosive periodswas calculated as about 500 yr longer (Swanson et al. 2014).

Single-criterion analogies for tectonic setting, rock geo-chemistry and volcano morphology give rise to many perfectanalogues to Kıl̄auea (i.e. analogy equal to one), given itsrelatively simple ID profile for those criteria (Fig. 3). In termsof eruption size, a large number of volcanoes share a highvalue of single-criterion analogy with Kıl̄auea (ASz =0.9989). Only one volcano (Piton de la Fournaise) has a slight-ly higher value of eruption-size analogy (ASz = 0.9992). Thisis related to the fact that, similarly to Kıl̄auea, over 99% of theeruptions at Piton de la Fournaise have beenVEI ≤ 2, but thereis also one large explosive event, a VEI 5 eruption (theBellecombe Ash Member eruption, Global VolcanismProgram 2013; although the eruption is contested by Ortet al. 2016, to have been actually three eruptions, adding upto volumes of around 0.3 km3—VEI 4—and column heightsof 8 km, at maximum). At Kıl̄auea, the largest explosive erup-tion in its eruptive record is a VEI 4 eruption (Keanakāko‘iash, 1790 AD; which is interpreted to have been a long-lastingseries of events instead of a single eruption, McPhie et al.1990; Mastin et al. 2004; Swanson et al. 2014; Swanson andHoughton 2018). In terms of eruption style, it is possible toidentify the top 10 analogue volcanoes to Kıl̄auea (Table 5).These are predominantly basaltic to dacitic volcanoes that, onaverage, are characterised by producing lava flows and/orfountaining in almost every eruption (> 92% of them), ballis-tics and tephra in 1 out of 3 eruptions, and phreatic/phreatomagmatic activity only occasionally (about 2% of theeruptions).

Multi-criteria searches of analogue volcanoes to Kıl̄aueawith scheme A (equal weight) bring a mixture of analogue

Table 4 List of the event types used from the GVP database and theirassigned correspondence in terms of 8 groups of physical hazardousprocesses

Event type (as in GVP) Group of physical processes

Lava flow(s) Lava flow and/or fountaining

Lava fountains Lava flow and/or fountaining

Fissure formation Lava flow and/or fountaining

Cinder cone formation Lava flow and/or fountaining

Scoria Lava flow and/or fountaining

Blocks Ballistics and tephra

Bombs Ballistics and tephra

Tephra Ballistics and tephra

Pumice Ballistics and tephra

Ash Ballistics and tephra

Lapilli Ballistics and tephra

Explosion Ballistics and tephra

Eruption cloud Ballistics and tephra

Phreatic activity Phreatic and phreatomagmatic activity

Phreatomagmatic eruption Phreatic and phreatomagmatic activity

Lahar or mudflow Water-sediment flows

Jokulhaup Water-sediment flows

Tsunami Tsunamis

Pyroclastic flow Pyroclastic density currents

Directed explosion Pyroclastic density currents

Edifice destroyed Edifice collapse/destruction

Caldera formation Caldera formation

Bull Volcanol (2019) 81: 76 Page 9 of 22 76

volcanoes (Table 5): some of them can be linked to top 10analogues in eruption size and style but others, like the top 1and 3 analogue volcanoes (Mauna Loa and Karthala, respec-tively), are not identified when using single-criterion searches.The top 10 list for scheme B (eruption size and style only) isdominated by the top 10 eruption-style analogues (Table 5),but the use of both eruption size and style provides new can-didates that do not arise in the single-criterion search: e.g.Mauna Loa and Hualālai. Finally, the top 10 list of analoguevolcanoes for scheme C (rock geochemistry and volcano mor-phology only) has a few examples from lists A and B but,generally, contains volcanoes that are not listed in the othersearches (Table 5). This suggests that these predominantlybasaltic volcanoes, with morphologies similar to Kıl̄auea,may not necessarily show eruption sizes and styles closelymatching those of Kıl̄auea volcano.

The ratios between different single-criterion analogies forthe top 20 analogue volcanoes identified from differentweighting schemes are shown in Fig. 4. It is noted that thefact that a weighting scheme uses two analogy criteria only

(e.g. eruption size and style for scheme B) does not imply thatthe identified top 20 analogues do not have data for the otheranalogy criteria (e.g. rock geochemistry or volcano morphol-ogy). Analogy in morphology and geochemistry are system-atically higher than analogy in either eruption size or style, forthe analogue volcanoes obtained with scheme C. Likewise,the analogue volcanoes derived from scheme B have system-atically higher values of analogy in eruption size and stylecompared with analogy in morphology and geochemistry(Fig. 4b, c). In other words, analogy in eruption size and styleand analogy in geochemistry and morphology for Kıl̄aueavolcano are decoupled: volcanoes with rock geochemistriesand/or morphologies the most similar to Kıl̄auea (top 20,scheme C) do not necessarily show the same highest de-gree of similarity in terms of eruption size and/or style (top20, scheme B). Otherwise, the values of the ratios betweenanalogy criteria would be very similar. Therefore, the de-gree of decoupling between different single criteria foreach volcano can be assessed as the dispersion or distancebetween data points for different weighting schemes.

Fig. 3 ID profiles for the three example volcanoes in the study, Kıl̄auea(USA), Fuego (Guatemala) and Sinabung (Indonesia), for (a) tectonicsetting and volcano morphology; (b) rock geochemistry (rock-type ab-breviations as in Fig. 1); (c) eruption size (VEI: Volcanic Explosivity

Index); (d) eruption style (LF: lava flows and/or fountaining; BT: ballis-tics and tephra; PH: phreatic and phreatomagmatic activity; WSF: water-sediment flows; TSU: tsunamis; PDC: pyroclastic density currents; DST:edifice collapse/destruction; CF: caldera formation)

Bull Volcanol (2019) 81: 7676 Page 10 of 22

Table 5 Top 10 analogue volcanoes to Kıl̄auea, Fuego and Sinabungvolcanoes, according to different single-criterion analogy metrics andthree different weighting schemes to assess multi-criteria analogy. ISOAlpha-2 country codes for each volcano are indicated between round

brackets. Number of eruptions with VEI assigned that are available inthe GVP database are reported between square brackets for each analoguevolcano in scheme B

Single-criterion analogy metri Muc lti-criteria analogy

Targetvolcano

Analoguevolcano

Tectonicsetting

Rockgeochemistry

Volcano morphology

Eruptionsize

Eruptionstyle

Scheme A Scheme B Scheme C

)SU(

aeualīK

#1 Many Many Many

Piton de laFournaise

(FR)Hengill (IS) Mauna Loa (US) Hengill (IS) [11] St. Paul (FR)

#2 Many Many Many Many Fremrinamar (IS)Piton de la

Fournaise (FR)

Fremrinamar

(IS) [2]

Île aux Cochons

(FR)

#3 Many Many Many Many Langjökull (IS) Karthala (KM)Langjokull

(IS) [6]Mere Lava (VU)

#4 Many Many Many Many Wolf (EC)Brennisteinsfjoll

(IS)Emuruangogolak

(KE) [6]Mauna Loa (US)

#5 Many Many Many Many Cerro Azul (EC) Ecuador (EC)Cerro Azul

(EC) [11]Raikoke (RU)

#6 Many Many Many ManyEmuruangogolak

(KE)Cerro Azul (EC) Krafla (IS) [27]

Brennisteinsfjoll(IS)

#7 Many Many Many Many Krafla (IS)Theistareykir

(IS)Mauna Loa(US) [110]

Golaya (RU)

#8 Many Many Many Many Dabbahu (ET) Wolf (EC) Wolf (EC) [11] Visokiy (RU)

#9 Many Many Many ManyIskut-Unuk

River Cones (CA)Prestahnukur

(IS)Hualālai(US) [22]

Latukan (PH)

#10 Many Many Many Many Torfajökull (IS) St. Paul (FR) Ghegam Ridge Wapi Lava Field (AM) [1] (US)

Targetvolcano

Analoguevolcano

Tectonicsetting

Rockgeochemistry

Volcano morphology

Eruptionsize

Eruptionstyle

Scheme A Scheme B Scheme C

Fueg

o(G

T)

#1 ManyGreat Sitkin

(US)Koryasky

(RU)Tenerife

(ES)Chikurachki

(RU)Klyuchevskoy

(RU)Momotombo

(NI) [16]Tacaná (MX-GT)

#2 ManySão Jorge

(PT)Kronotsky

(RU)Pagan(US)

Pavlof(US)

Semeru (ID) Pagan (US) [17] Koryaksky (RU)

#3 ManyGaribaldi

Lake (CA)Baker(US)

Llaima(CL)

Momotombo (NI) Osorno (CL) Pavlof (US) [42] Kronotsky (RU)

#4 Many

Michoacán-Guanajuato

(MX)

Tacaná(MX-GT)

Rincón de laVieja (CR)

Pacaya(GT)

Merbabu (ID)Klyuchevskoy

(RU) [101]Kamen (RU)

#5 ManyMount St

Helens (US)Tajumulco

(GT)Asamayama

(JP)Villarrica

(CL)Tacaná (MX-GT)

Karangetang(ID) [53]

Klyuchevskoy(RU)

#6 ManyLamongan

(ID)Santa Maria

(GT)Manam

(PG)Semeru

(ID)Chikurachki

(RU)Villarrica

(CL) [123]Merbabu (ID)

#7 ManyKasuga 2

(US)Acatenango

(GT)Momotombo

(NI)Karymsky (RU) Pavlof (US)

Semeru(ID) [58]

Semeru (ID)

#8 ManyLa Gloria

(MX)Sangay

(EC)Fujisan

(JP)Karangetang (ID) Baker (US)

Lewotobi(ID) [23]

Mayon (PH)

#9 Many Chichinautzin Lanín Reykjanes Klyuchevskoy Acatenango (GT) Karymsky Vilyuchik (RU)

(MX) (CL-AR) (IS) (RU) (RU) [40]

#10 Many ManyArenales

(CL)Many Towada (JP) Shishaldin (US)

Ambrym(VU) [49]

Sangay (EC)

Bull Volcanol (2019) 81: 76 Page 11 of 22 76

The spatial distribution of the top 20 analogue volca-noes to Kı l̄auea, according to the three weightingschemes is displayed in Fig. 5a–c. The vast majorityof analogues from schemes A (20/20) and B (13/20)are located either on intraplate settings, such as oceanicislands (e.g. Galapagos, Comoros) or on rift zones (e.g.Iceland, East African Rift). This spatial clustering ofvolcanoes away from subduction zones is a non-random pattern. Approximately 70% of the volcanoesin the GVP database are located on subduction zones.Therefore, if 20 volcanoes were sampled at random, 14volcanoes would be located, on average, on subductionzones. This number is significantly above the number ofanalogue volcanoes obtained for Kıl̄auea in schemes Aand B. In scheme C, the analogue volcanoes are moredispersed spatially and they can also occur on subduc-tion zones (Fig. 5c). These volcanoes are purely basalticstratovolcanoes on the western rim of the Pacific plateand whose values of M are slightly above the meanvalue for complex stratovolcanoes and therefore closerto the mean value of shield volcanoes (Table 3).

Kıl̄auea is a below-average shield volcano in terms ofmorphology (M = 0.447; Table 3). Therefore, a greaterproportion of stratovolcanoes will have M values similarto Kıl̄auea, compared with other shield volcanoes withhigher M values (see Fig. 2c).

Fuego, Guatemala

Fuego is a basaltic-andesitic stratovolcano related to the sub-duction of the Cocos plate under the Caribbean plate andforms part of a lineament of volcanic centres that includesthe mainly Pleistocene Meseta volcano and Fuego’s twin vol-cano: Acatenango (Rose et al. 1978; Chesner and Rose 1984;Chesner and Halsor 1997). Volcanism has migrated spatially,from north to south, and chemically, from andesitic to basalticcompositions, with time (Chesner and Rose 1984). Historicalvolcanic activity has been mostly sourced from Fuego and haspredominantly consisted of open-conduit, persistent, and fre-quent explosive activity (from Strombolian to Vulcanian)punctuated by larger eruptions up to sub-Plinian (Rose et al.

Table 5 (continued)

Target volcano

Analogue volcano

Tectonic setting

Rock geochemistry

Volcano morphology

Eruptionsize

Eruptionstyle

Scheme A Scheme B Scheme C

)DI(

gnubaniS

#1 Many Many Many Many Sanbesan (JP) San José(CL-AR)

Hunga Tonga-Hunga Ha’apa

(TO) [5]Matutum (PH)

#2 Many Many Many Many Nijima (JP)San Pedro-

San Pablo (CL)Niijima (JP) [2] Little Sitkin (US)

#3 Many Many Many Many Rausudake (JP)Tandikat-

Singgalang (ID)Victory (PG) [1] Atacazo (EC)

#4 Many Many Many Many Loloru (PG) Peuet Sague (ID)Suretamatai

(VU) [3]San Pedro-San

Pablo (CL)

#5 Many Many Many Many Kuchinoshima (JP) Chiginagak (US)Tomariyama/

Golovnin(JP/RU) [1]

Acamarachi (CL)

#6 Many Many Many Many

Nevados Ojosdel Salado(CL-AR)

Kerinci (ID) Egon (ID) [5]San José(CL-AR)

#7 Many Many Many Many Atacazo (EC) Sabancaya (PE) Callaqui (CL) [2]Tandikat-

Singgalang (ID)

#8 Many Many Many Many Tacaná (MX-GT) Turrialba (CR) Sundoro (ID) [9] Zimina (RU)

#9 Many Many Many Many

Hunga Tonga-Hunga Ha’apa

(TO)

Zhupanovsky (RU)

Miravalles(CR) [1]

Dutton (US)

#10 Many Many Many Many Iraya (PH)Guagua

Pichincha (EC)Peuet Sague

(ID) [7]Nevado del Ruiz

(CO)

Black bold text: analogue volcanoes ranked top 10 by schemeA. Blue bold text: analogue volcanoes ranked top 10 by schemeB. Red bold text: analoguevolcanoes ranked top 10 by scheme C. Blue-background cell: analogue volcanoes ranked top 10 by schemes A&B. Red-background cell: analoguevolcanoes ranked top 10 by schemes A&C. Black-background cell: analogue volcanoes ranked top 10 by all the weighting schemes

Bull Volcanol (2019) 81: 7676 Page 12 of 22

1978; Martin and Rose 1981; Lyons et al. 2010; Naismithet al. 2019).

Tectonic setting is a non-differentiating criterion for asubduction-zone volcano like Fuego. All the other singlecriteria can be used to identify a set of top 10 analogue volca-noes to Fuego (Table 5). Those analogues according to volca-no morphology are perfect analogues because Fuego is one ofthe 11 volcanoes in the morphological database with a valueof M = 0. These volcanoes have very high values of H andH/W* and, at the same time, very small values of T and d. Thetop 10 eruption-style analogue volcanoes (Table 5) produceballistics and tephra, and lava flows and/or fountaining on98% and over 30% of their eruptions, on average. Water-sediment flows and PDCs are generated, respectively, in11% and 13% of their eruptions, on average. Finally, the av-erage percentage of eruptions with collapse/destruction of the

edifice or with caldera formation is 0.6% and 0.3%,respectively.

The top 10 analogue volcanoes according to schemeA tendto be related to volcanoes with high values in analogy mor-phology or eruption style (Table 5). In scheme B, the top 10analogue volcanoes tend to appear in the top 10 list of eruptionstyle analogues as well. However, their analogy in eruptionsize is also high, because their ASz/ASt ratio is very close to 1(Fig. 4d). The values of multi-criteria analogy in scheme Cseem to be closely linked with high values of analogy in mor-phology while none of the rock-geochemistry top 10 analoguevolcanoes appears in the lists from scheme A, B or C(Table 5). Nevertheless, the analogy in geochemistry seemsto be better coupled with the analogy in eruption size and styleas it is shown by the analogue volcanoes for scheme B in Fig.4e, f. The large scatter in the values of the ratios that involve

Fig. 4 Ratios between single-criterion volcano analogies for the top 20analogue volcanoes to Kıl̄auea, USA (a–c); Fuego, Guatemala (d–f); andSinabung, Indonesia (g–i), according to three different weightingschemes to calculate multi-criteria volcano analogies: all criteria, equal-weight (scheme A); eruption size and style only (scheme B); and rockgeochemistry and volcano morphology only (scheme C). Note that, evenif a given weighting scheme uses only two criteria (e.g. scheme B), the

identified analogue volcanoes can have data for all the analogy criteriaand, thus, the analogy ratios can be calculated for any of these criteria.The different quadrants in the graphs show which criteria are dominant inthe process of identifying analogue volcanoes to the specific target vol-cano. ATs: analogy in tectonic setting; AG: analogy in rock geochemistry;AM: analogy in volcanomorphology; ASz: analogy in eruption size; ASt:analogy in eruption style

Bull Volcanol (2019) 81: 76 Page 13 of 22 76

the analogy in morphology suggests that volcanoes thathave eruption sizes and styles similar to Fuego do nothave particularly similar morphologies. Somewhatequivalently, the analogue volcanoes for scheme C showa greater scatter along the AM/ASt ratio (y-axis, Fig.4e) than along the AG/ASt ratio (x-axis, Fig. 4f): thatis, volcanoes with morphologies similar to Fuego havemore varied eruption styles, compared with Fuego thanvolcanoes with rock geochemistries similar to Fuego.Three volcanoes are listed in two different schemes:Tacaná and Merbabu (schemes A, C; the latter is nottop 10 in any single-criterion search) and Pavlof(schemes A, B); and two volcanoes are listed in allthree weighting schemes: Semeru and Klyuchevskoy.

Spatially, the analogue volcanoes to Fuego are located onsubduction zones, independently of whether tectonic setting isused (scheme A) or not (schemes B and C) as a search crite-rion (Fig. 5d–f). These spatial distributions are also non-random because the number of volcanoes on subduction zones(from 18 to 20) is significantly higher that what could beexpected, on average, if the locations of 20 volcanoes wererandomly sampled from the GVP database. The analogue vol-canoes in schemes A and B are relatively evenly distributedalong the western coast of the American continents, the west-ern edge of the Pacific plate (especially in scheme B) and

Indonesia. In scheme C, half of the top 10 analogue volcanoesare located in Kamchatka, Russia.

Sinabung, Indonesia

Sinabung is an andesitic-to-dacitic stratovolcano related to theoblique subduction of the Indo-Australian plate under theEurasian plate along the island of Sumatra (Diament et al.1992), and it is located less than 40 km away from thenorth-western edge of Lake Toba caldera. Volcanic activityat Sinabung was relatively unknown, and had been absentfor the last 400 years, before its first historical eruption oc-curred in 2010 (Gunawan et al. 2019). After 3 years of repose,the volcano again erupted in 2013, this time evolving into along-term (~ 5 years) eruption, which included initial phreaticand phreatomagmatic phases, several periods of lava-domegrowth and collapse, andesitic lava flows and (cyclic)Vulcanian explosions (Gunawan et al. 2019; Nakada et al.2019; Pallister et al. 2019).

In general, single-criterion searches are extremely uninfor-mative for Sinabung because it has an ID profile (Fig. 3) that isvery similar to many other volcanoes in the databases, whenlooking at single-criterion analogy only. For instance, thereare hundreds of volcanoes on a subduction zone under conti-nental crust and many tens of volcanoes with rock

Fig. 5 Spatial distribution of the top 20 analogue volcanoes to Kıl̄auea, USA (a–c); Fuego, Guatemala (d–f); and Sinabung, Indonesia (g–i), according tothe multi-criteria analogy metrics calculated via three different weighting schemes. Plate boundaries taken from Bird (2003)

Bull Volcanol (2019) 81: 7676 Page 14 of 22

geochemistry evenly distributed between andesite and dacite.The only single criterion that provides a list of top 10 analoguevolcanoes to Sinabung is eruption style (Table 5).

Multi-criteria searches bring much more information be-cause the number of volcanoes that share the very same char-acteristics to the target volcano, for several single criteria, ismuch lower. The analogue volcanoes according to scheme Aarise from a combination of all the criteria and they are alldifferent from the list of analogue volcanoes obtained fromthe analogy in eruption style. They display a relatively clus-tered pattern (with some outliers) around the (1,1) point ac-cording to different ratios between single criteria (Fig. 4g–i),which suggests that the values of all single-criterion analogiesare comparable. These top 10 scheme-A analogue volcanoes(Table 5) show the following characteristics: (i) they all are onsubduction zones under continental crust; (ii) their expectedgeochemistry is predominantly andesitic to dacitic; (iii) theyhave morphologies significantly below the average morphol-ogy of stratovolcanoes (mean value on M = 0.172); (iv) theiraveraged distribution of eruption sizes is dominated by VEI ≤2 eruptions but VEI 3+ eruptions have non-negligible proba-bilities of occurrence (8%, in particular); and (v) their aver-aged hazardous phenomenology indicates that relatively feweruptions would produce lava flows and/or fountaining (4%),water-sediment flows (2%) or PDCs (9%). The latter is instark contrast with the eruption-style profile of Sinabung, es-pecially for PDCs, which have been reported in 67% of theeruptions. Nevertheless, the eruption data for Sinabung isstrongly deficient, with only two eruptions with a VEI sizeassigned and three eruptions with hazardous phenomena re-corded in the GVP database (and no reference to phreatic/phreatomagmatic activity or lava flows for the 2013–2018eruption; GVP 2013). This potential issue is tackled in thenext section.

The set of top 10 analogue volcanoes from scheme B in-cludes some of the volcanoes identified with the single-criterion search of analogy in eruption style. Still, the majorityof multi-criteria analogue volcanoes are not listed in thesingle-criterion search (Table 5). The analogue volcanoesfrom scheme C are also different from the single-criterionanalogues, apart from the case of Atacazo (Table 5). Thisvolcano is a perfect analogue according to tectonic setting,rock geochemistry and morphology and a top 10 analogue interms of eruption style.

In terms of the spatial distribution, the analogue volcanoesto Sinabung are always located on subduction zones, indepen-dently of whether tectonic setting is used as analogy criterionor not. As in the case of Fuego volcano, this represents a non-random spatial distribution. These analogues are distributedsimilarly in schemes A and C (Fig. 5g, i), with the westerncoast of South America and Indonesia dominating over otherareas (10 out of 17 different analogue volcanoes are locatedthere). Among them, three volcanoes appear as top 10

analogue volcanoes according to both scheme A and C: SanJosé, San Pedro-San Pablo and Tandikat-Singgalang. Inscheme B (Fig. 5h), the analogue volcanoes to Sinabung ap-pear to be more scattered and on different areas compared toschemes A and C. Some of these analogue volcanoes may notbe fully representative because of the issues with the eruptiondata for Sinabung explained before.

Interestingly, the distribution of VEI sizes for Kıl̄auea (forwhich tens of eruptions are recorded in the GVP database) isalmost identical to the (incomplete) distribution for Sinabung(Fig. 3c). Therefore, the differences observed in the sets ofanalogue volcanoes to Kıl̄auea and Sinabung using schemeB (Fig. 5b, h) can only be explained in terms of eruption style.Even though the eruption-style data for Sinabung are alsoincomplete, the hazardous phenomenology recorded at thetwo volcanoes is remarkably disparate (Fig. 3d). Thus,Kıl̄auea shows the typical profile of a lava-flow-producingvolcano while Sinabung can be ascribed to the profile of atephra-and-PDC-producing volcano. Accordingly, the ana-logue volcanoes to Kıl̄auea and Sinabung derived fromscheme B are still fundamentally different in terms of tectonicsetting (Fig. 5b, h), rock geochemistry and even morphology(e.g. mean(M) = 0.541 for the Kıl̄auea analogues andmean(M)= 0.298 for the Sinabung analogues).

Discussion

Volcanic hazard assessment

VOLCANS represents a new objective method for identifyingsets of analogue volcanoes, for a given volcano of interest,using global volcanological databases. This type of automatedand flexible procedure to extract sets of analogue volcanoeshas the potential to become a fundamental tool used to informvolcanic hazard assessments, during quiescent, unrest and cri-sis phases. Existing methods and tools such as (Bayesian)event trees (Newhall and Hoblitt 2002; Marzocchi et al.2008, 2010; Newhall and Pallister 2015), Bayesian BeliefNetworks (Aspinall et al. 2002; Hincks et al. 2014; Tierzet al. 2017) or hierarchical Bayesian modelling (Ogburnet al. 2016) would extremely benefit from deriving its priordistributions from objective sets of analogue volcanoes(Sheldrake 2014; Biass et al. 2016). Similarly, alternativeparameterisations of the hazard models could be built fromdifferent sets of analogue volcanoes and this could be usedto quantify the epistemic uncertainty and/or for testing of haz-ard models (e.g. Marzocchi and Jordan 2014; Spiller et al.2014; Tierz et al. 2016a, 2016b). The presented method canalso be used to enlarge the datasets used in the hazard assess-ment. Up to now, the common practice has been to use datafrom a limited set of best analogue volcanoes to assess volca-nic hazard (e.g. Marzocchi et al. 2004; Sandri et al. 2012;

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Tierz et al. 2016a; Wright et al. 2019). With VOLCANS, thehazard analyst could expand the dataset to any available vol-cano and weigh the data according to the multi-criteria analo-gy calculated between these volcanoes and the target volcano.In this way, data from good analogueswould count more thandata from other volcanoes. This would dramatically increasethe amount of data available for the hazard assessment, hence,improving the robustness of the statistics computed (e.g.Newhall and Hoblitt 2002; Marzocchi et al. 2008, 2010;Ogburn et al. 2016). Still, if selecting the best analoguevolcanoes is the preferred strategy for the hazard analysis,VOLCANS can also help define such a set: e.g. top 10, top20, volcanoes above a given threshold of volcano analogy.Volcano analogy can be computed using any possible multi-criteria weighting scheme, depending on the particular needsand requirements of the user of the method. This flexibilityhelps with adaptation and application to different situationsand volcanological problems. Nonetheless, there will alwaysbe the need to assess the significance of the analogue setsfound independently (Newhall et al. 2017) as well as to sup-plement the results with relevant expert scientific knowledgenot available in the databases (Aspinall et al. 2002, 2003;Selva et al. 2012; Hincks et al. 2014; Newhall and Pallister2015).

A tool to complement expert-derived analoguevolcanoes

The hazard analyst/team may also be interested in assessingthe general appropriateness of sets of analogue volcanoes thatwere selected, a priori, during previous crises and/or hazardevaluations (e.g. Marzocchi et al. 2004; Sandri et al. 2012;Newhall and Pallister 2015). Here, this is exemplified bylooking at the values of multi-criteria analogy calculated forvolcanoes that have been taken as analogues to the three ex-ample volcanoes by previous published and unpublished stud-ies. In particular: Piton de la Fournaise (France) and Etna(Italy) for Kıl̄auea (Peltier et al. 2015; Poland et al. 2017);Villarrica, Llaima (Chile), Pacaya (Guatemala), Reventadorand Tungurahua (Ecuador) for Fuego (Eliza Calder, unpub-lished data); and Unzen (Japan), Soufrière Hills (Montserrat),Nevado del Huila (Colombia), Guagua Pichincha (Ecuador)and Redoubt (USA) for Sinabung (Heather Wright, pers.comm., October 12, 2018).

For all three volcanoes, the multi-criteria analogy valuesand the percentage of volcanoes in the GVP database thatare better analogues than the selected a priori analogues areanalysed. This percentage can be calculated as follows: (1) foreach target volcano and weighting scheme, a value of multi-criteria analogy can be calculated between the target volcanoand any volcano in the GVP database; (2) the value of multi-criteria analogy for a given a priori analogue volcano corre-sponds with a specific percentile of the distribution of all

multi-criteria analogy values; (3) one minus this percentileprovides the percentage of better analogues (i.e. those withhigher multi-criteria analogy than the a priori analogue).Additionally, and in the case of Fuego, an analysis on howsensitive the results of VOLCANS are to changes in the erup-tive record of the target volcano has been carried out. Thisanalysis shows that the method is quite stable even whenadding or removing up to 15 eruptions from this eruptiverecord (see Online Resources 7 and 8).

Kı̄lauea, USA

The highest multi-criteria analogy occurs between Kıl̄aueaand Piton de la Fournaise, independently of the weightingscheme used (Fig. 6a). For instance, their morphology is quitesimilar (Kıl̄auea, M = 0.447; Piton de la Fournaise, M =0.395), even though Kıl̄auea is volumetrically one order ofmagnitude larger than Piton de la Fournaise (Peltier et al.2015). This could be related to geochemistry and/or eruptionstyle: e.g. their edifices are principally built from lava flows,with low proportions of pyroclastic material (de Silva andLindsay 2015). In the case of Etna, several reasons accountfor its lack of similarity with Kıl̄auea. For example, the rocktypes in the GVP database capture the predominantly alkalineproducts of Etna (Correale et al. 2014; Corsaro and Métrich2016) and this clearly separates this volcano from thetholeiitic-dominated Kıl̄auea and Piton de la Fournaise(Clague and Dalrymple 1987; Albarède et al. 1997).Considering the three volcanoes, eruption size and style arethe criteria that better match across them (Fig. 6a).Significantly, all three volcanoes are reported to have pro-duced tsunamis, something that is coherent with their long-term flank instability (Poland et al. 2017).

The percentages of better analogues significantly changeacross the different multi-criteria weighting schemes,highlighting the fact that some volcanoes can be goodanalogues in terms of some criteria but not according to others(Sheldrake 2014; Newhall et al. 2017). For instance, Etna maybe a relatively good analogue in terms of eruption size andstyle, i.e. less than 10% of the Holocene volcanoes are betteranalogues. However, in terms of morphology and geochem-istry, more than half of the Holocene volcanoes are betteranalogues to Kıl̄auea than Etna (Fig. 6b).

Fuego, Guatemala

The best a priori analogue volcanoes to Fuego are Villarricaand Llaima, in Chile, regardless of the weighting scheme used(Fig. 6c). Geochemistry and, especially, morphology play asignificant role in this as it is observed by the lower percent-ages of volcanoes that are better analogues than these twowhen scheme C is considered (Fig. 6d). Pacaya andTungurahua display opposite patterns: the former is the best

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analogue after Villarrica and Llaima according to scheme Band the latter is the best analogue after those two according toscheme C. However, Pacaya is the least analogous to Fuegoaccording to scheme C and Tungurahua is the least analogousaccording to scheme B (Fig. 6d). This would reinforce thedecoupling between morphology (and maybe geochemistry)and eruption size and style observed for the top 20 analoguesof Fuego in Fig. 4e, f. Further research would be required tounderstand this pattern.

Sinabung, Indonesia

The best analogue to Sinabung volcano, when taking intoaccount all the criteria, is Guagua Pichincha, followed byNevado del Huila and Unzen (Fig. 6e). Only 1 to 4% of theHolocene volcanoes are better analogues, according to theGVP data (Fig. 6f). Interestingly, Nevado del Huila is the leastanalogous of the five selected a priori analogue volcanoeswhen eruption size and style are evaluated (scheme B).Soufrière Hills and Redoubt are not particularly goodanalogues because their morphologies are more complex(i.e. larger M values) and because their rock types are notexclusively andesites and dacites. Also eruption-style dataplays a role in the volcano analogy but the data for Sinabung

are not properly recorded in the version of the GVP databaseused in this analysis. That is, no lava flows or water-sedimentflows are reported in the ID profile (Fig. 3) even though theydid occur during the 2013–2018 eruption (Gunawan et al.2019; Nakada et al. 2019).

To test how the values of volcano analogy may vary if theprofile of Sinabung is modified, the following changes areapplied: (1) lava flows and lahars from the 2013–2018 eruptionare included; and (2) the 2013–2018 eruption is updated to VEI4 (GVP, 2013, database version 4.7.4). Results are very stablefor scheme A, even for the percentage of better analogues(maximum change of 2%, Fig. 7). This is partly due to theeruption size and style having a combined weight of 40% inthe calculation of the multi-criteria analogy. Obviously, schemeB is the one that changes the most and the differences in per-centage of better analogues can be up to 11%. The result ofupdating Sinabung’s profile is that of systematically reducingthe percentage of better analogue volcanoes, with the excep-tion of Redoubt. This decrease in the percentage can be ex-plained by the fact that there are many more volcanoes in theGVP database with distributions of eruption sizes very domi-nated by VEI ≤ 2 eruptions (Sinabung’s GVP 4.6.7 profile)than volcanoes with distributions with substantial frequencyof VEI 4 eruptions (Sinabung’s GVP 4.7.4 profile).

Fig. 6 Quantitative assessment of some volcanoes thought to be goodanalogues, a priori, to the three example target volcanoes. a, c, e: valuesof multi-criteria volcano analogy (AXapriori, where X denotes the examplevolcano) according to three different weighting schemes. The contribu-tion of each single criterion to the total analogy is shown by the differentcolours (abbreviations as in Fig. 4). b, d, f: exceedance probability of

AXapriori, calculated from the distribution of multi-criteria volcano analo-gy values (AXY) between each example volcano, X, and any volcano Y inthe GVP database. This probability can be understood as the percentageof all the volcanoes in the GVP database that are better analogues thaneach of the a priori analogue volcanoes, according to three differentweighting schemes

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Therefore, the updated profile makes the a priori analogues tobe more unique analogues of Sinabung.

Commonalities in unique volcanoes

The presented method can also be applied to investigate com-monalities in unique volcanic systems (Cashman and Biggs2014), thus aiding research on how volcanoes work. For ex-ample, if two or more data-poor volcanoes are identified to begood general analogues to each other, further research on oneof them may serve to (1) ensure this volcano analogy holdswhen more data are collected, and (2) use the data from one ofthe volcanoes as proxy for the other volcano. This researchmay be guided by prioritising research on volcanoes that seemto be analogues to one or more high-relevance volcanoes (e.g.persistently active volcanoes with seasonal lahar activity:Fuego and Semeru; Lyons et al. 2010; Thouret et al. 2014).Other findings of analogue volcanoes can also provide hintsabout magmatic or physical volcanic processes. Further ded-icated research could be targeted at exploring and understand-ing some general observations derived from VOLCANS. Forinstance, analogue volcanoes to Kıl̄auea are located on ocean-ic islands or rifting settings when all the criteria are used(schemeA, Fig. 5a) but can also be found on subduction zoneswhen morphology and rock geochemistry are the only criteriaused (scheme C, Fig. 5c). In the case of Fuego, onlysubduction-zone volcanoes are top 20 analogues when using

all criteria but one oceanic-island volcano (Pico, Azores) ap-pears when using morphology and geochemistry (Fig. 5d, f).On the contrary, all analogue volcanoes to Sinabung are locat-ed on subduction zones, independently of the criteria used(Fig. 5f–i). Given that primary (mantle) magmas are exclu-sively of basaltic composition (Rogers 2015), the latter type ofvolcanism can occur on any tectonic setting (and probablytype of volcano) while more silicic volcanism is restricted toareas wheremagma ascends slowly and/or stagnates and, thus,crustal anatexis, magma differentiation (and segregation) and/or crustal assimilation are promoted (Annen et al. 2005;Bachmann et al. 2007; Hutchison et al. 2018). Also,Kıl̄auea’s morphology, expressed as its M value, is similar tomany volcanoes in the databases (Figs. 2c, 3a) and, therefore,those volcanoes may occur in varied tectonic settings (Fig.5c). On the contrary, the very-low M values of Fuego andSinabung are shared by fewer volcanoes in the databases(Figs. 2c, 3a) and those tend to be restricted to subduction-zone settings, where magmatic conditions and volcanic pro-cesses favour the development of such morphologies (Grosseet al. 2009; de Silva and Lindsay 2015).

Analogue volcanoes and global datasets

Tectonic setting, rock geochemistry and morphology may bemore stable criteria than eruption size and style to search forgeneral analogues, unless there are profound changes like

Fig. 7 Comparison between thevalues of multi-criteria volcanoanalogy, AXapriori, and the valuesof exceedance probability ofAXapriori, for the a priori analoguevolcanoes to Sinabung (H.Wright, pers. comm., October 12,2018) when using two differentID profiles for the target volcano.a, b: ID profile stored in the GVPdatabase, version 4.6.7 (see Fig.3); c, d: ID profile obtained afterupgrading the 2013–2018 to VEI4 and adding lava flows and la-hars as phenomenology that hap-pened during the aformentionederuption (Gunawan et al., 2019;Nakada et al., 2019; GVPdatabase, version 4.7.4)

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those inmorphology linkedwith the partial or total destructionof the edifice (Cioni et al. 1999; Belousov et al. 2007).Eruption size and style data will depend more strongly onunder-recording (Mead and Magill 2014; Sheldrake 2014;Rougier et al. 2016), under-/mis-reporting and data discovery(Loughlin et al. 2015). Emphasis should be placed on thor-oughly double-checking the inclusion of unequivocal data forall relevant hazardous phenomena occurring during a giveneruption, from reports released by volcano observatories.Reporting itself should also ensure that the occurrence of allhazardous phenomena is properly recorded. Moreover, theimportance of using a standardised (multilingual) nomencla-ture in reporting eruptive phenomena must be re-assessed, tocircumvent some of the difficulties that using the availabledata currently implies. For example, the term “caldera collapse”can be equally used to describe purely effusive or VEI 7+eruptions (Branney and Acocella 2015; Gudmundsson et al.2016). In spite of the aforementioned issues, VOLCANS is aflexible tool that allows the user to give different weights toeach criteria to decrease the influence of inaccurate data, forinstance. It also permits rapid updating of the volcano ID pro-files and, hence, re-calculation of volcano analogies as new databecome available (Fig. 7).

Conclusions

We present the VOLCano ANalogues Search tool(VOLCANS), an approach with which to explore and quanti-fy the similarity between volcanic systems at a global scale bymaking use of three separate volcanological databases. Thekey outcome of the method is the objective (i.e. data-driven),structured and reproducible quantification of the degree ofvolcano analogy among any two volcanic systems listed inthe Global Volcanism Program database. This approach canbe used to derive informative sets of analogue volcanoes and/or to evaluate the appropriateness of volcanoes selected asanalogues through other means, e.g. expert judgement. Theapplication of VOLCANS is illustrated for three different vol-canoes with significant recent or ongoing eruptions (Kıl̄auea,USA; Fuego, Guatemala; and Sinabung, Indonesia).Specifically, we find that:

i. Analogy in volcanomorphology can be fully quantified byusing simplified variables for dimensions of volcanic edi-fices: a continuum in morphologies arises from thedatasets (Grosse et al. 2014), but different types of volcanohave values of a unified morphological variable that fol-low different probability distributions;

ii. Depending on the characteristics of the target volcano,some criteria may be non-differentiating, that is: they arenot effective differentiators of small sets of analogue vol-canoes because there are too many volcanoes with similar

characteristics. Whether a particular analogy criterion isnon-differentiating, varies on a volcano to volcano basis;

iii. Sets of analogue volcanoes identified from multi-criteriasearches can include, as top analogues, volcanoes that arenot included in the sets of top analogues identified usingonly single-criterion analogy metrics;

iv. Plausible sets of analogue volcanoes can be obtainedusing as little as two criteria (e.g. eruption size and style,schemeB), even in cases where data for one of the criteriacould be suspected as being deficient (e.g. eruption sizefor Sinabung), provided that data for the other criteriaencode effective differentiators. For example, sets of an-alogue volcanoes for Sinabung and Kıl̄auea in scheme Bare differentiated mostly because of the frequent genera-tion of PDCs at Sinabung compared with Kıl̄auea. Ingeneral, analogue searches using more than one analogycriterion provide quite stable results of VOLCANS;

v. The spatial distributions of top analogue volcanoes follownon-random patterns even when tectonic setting is notused as a criterion for volcano analogy. For instance, atleast 38 out of 40 analogue volcanoes to Fuego andSinabung are located on subduction zones when usingeruption size and style only (scheme B) and rock geo-chemistry and volcano morphology only (scheme C) asthe analogy criteria;

vi. The degree of decoupling between different criteria ofvolcano analogy can be assessed through the dispersionin the ratios of single-criterion analogy metrics, whenusing different multi-criteria weighting schemes: themore similar the ratios for different schemes (i.e. themore clustered), the more coupled the analogy criteria.

Future applications of VOLCANS may be targeted atgaining a better understanding of the similarities and differ-ences between volcanic systems and/or at improving volcanichazard assessment, especially for those volcanoes that are da-ta-poor.

Acknowledgements We earnestly thank Sébastian Biass and an anony-mous reviewer for their thorough reviews and Christopher Gregg for hisextremely valuable comments and editorial handling. All the input re-ceived helped us improve the clarity and quality of the manuscript sub-stantially. We sincerely thank Benjamin Andrews and Edward Venzke forassistance in the use and content of the GVP database; and HeatherWright for kindly sharing her knowledge about analogue volcanoes ofSinabung and for valuable discussions. Finally, we would like to warmlythank many colleagues with whom we have shared fruitful discussionsabout volcanic systems, their analogies and dissimilarities: Sarah Ogburn,Susanna Jenkins, Ben Clarke, Charlotte Vye-Brown, Sam Engwell, JuliaCrummy, Max Van Wyk de Vries, Luigi Passarelli, Laura Sandri, IsabelMarín, Teresa Ubide, David Pyle, Fabien Albino, Matthieu Kervyn,Elaine Spiller, Robert Wolpert, Larry Mastin, Cynthia Gardner, JacobLowenstern, Wes Thelen, John Pallister, Alexa Van Eaton, Peter Kelly,Jim Vallance, John Ewert and the VDAP team and CVO as a whole.Published with permission of the Executive Director of BritishGeological Survey (NERC-UKRI).

Bull Volcanol (2019) 81: 76 Page 19 of 22 76

Authors’ statement The data supporting the conclusions are shown inthe figures and tables presented. Interested readers will find additionalfigures, tables, and data sets in the Electronic SupplementaryMaterial. Onrequest, the authors can also provide MATLAB (MATLAB, 2012) filescontaining more specific results or used to produce the figures.

PT, SL and EC conceived the study. PT processed the data, analysedthe results, prepared the figures and wrote themanuscript, with input fromthe other authors. All authors read, reviewed, and approved the finalversion of the manuscript.

Funding information The research leading to these results has receivedfunding from the UK Natural Environment Research Council RiftVolcanism: Past, Present and Future (RiftVolc) project (grant NE/L013460/1).

Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges weremade. The images or other third party material in this articleare included in the article's Creative Commons licence, unless indicatedotherwise in a credit line to the material. If material is not included in thearticle's Creative Commons licence and your intended use is notpermitted by statutory regulation or exceeds the permitted use, you willneed to obtain permission directly from the copyright holder. To view acopy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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